Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02986 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to inverse problems, such as Deep Image/Inverse Prior, and trained with inertia featuring both viscous and geometric Hessian-driven dampings. We study both the continuous-time case, i.e., the trajectory of a dynamical system, and the discrete case leading to an inertial algorithm with an adaptive step-size. We show in the continuous-time case that the network can be trained with an optimal accelerated exponential convergence rate compared to the rate obtained with gradient flow. We also show that training a network with our inertial algorithm enjoys similar recovery guarantees though with a less sharp linear convergence rate.